Assume B is a Boolean algebra with operations $+$ and $*.$ Let a be an element of b$.$ Assume p is a statement variable. Let t represent a tautology and c a contradiction. Assume C and D are subsets of some universal set U $.$

From the list below, select every sentence that must be true.

A$.$ The Boolean operation $+$ generalises the logic operation $^.$

B$.$ Boolean element $1$ behaves exactly the same as the integer $1.$

C$.$ The Boolean element $0$ corresponds to the empty set.